Database of modular polynomials

This module gives access to the database of modular polynomials. To use the database, you need to install the optional database_kohel package by the Sage command

sage -i database_kohel

EXAMPLES:

Sage

sage: # optional - database_kohel
sage: DBMP = ClassicalModularPolynomialDatabase()
sage: f = DBMP[29]
sage: f.degree()
58
sage: f.coefficient([28,28])
400152899204646997840260839128

Python

>>> from sage.all import *
>>> # optional - database_kohel
>>> DBMP = ClassicalModularPolynomialDatabase()
>>> f = DBMP[Integer(29)]
>>> f.degree()
58
>>> f.coefficient([Integer(28),Integer(28)])
400152899204646997840260839128

AUTHORS:

• David Kohel (2006-08-04): initial version

class sage.databases.db_modular_polynomials.AtkinModularCorrespondenceDatabase

Bases: ModularCorrespondenceDatabase

model = 'AtkCrr'

class sage.databases.db_modular_polynomials.AtkinModularPolynomialDatabase

Bases: ModularPolynomialDatabase

The database of modular polynomials Phi(x,j) for \(X_0(p)\), where x is a function on invariant under the Atkin-Lehner invariant, with pole of minimal order at infinity.

model = 'Atk'

class sage.databases.db_modular_polynomials.ClassicalModularPolynomialDatabase

Bases: ModularPolynomialDatabase

The database of classical modular polynomials, i.e. the polynomials Phi_N(X,Y) relating the j-functions j(q) and j(q^N).

model = 'Cls'

class sage.databases.db_modular_polynomials.DedekindEtaModularCorrespondenceDatabase

Bases: ModularCorrespondenceDatabase

The database of modular correspondences in \(X_0(p) \times X_0(p)\), where the model of the curves \(X_0(p) = \Bold{P}^1\) are specified by quotients of Dedekind’s eta function.

model = 'EtaCrr'

class sage.databases.db_modular_polynomials.DedekindEtaModularPolynomialDatabase

Bases: ModularPolynomialDatabase

The database of modular polynomials Phi_N(X,Y) relating a quotient of Dedekind eta functions, well-defined on X_0(N), relating x(q) and the j-function j(q).

model = 'Eta'

class sage.databases.db_modular_polynomials.ModularCorrespondenceDatabase

Bases: ModularPolynomialDatabase

class sage.databases.db_modular_polynomials.ModularPolynomialDatabase

Bases: object